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Global Well-Posedness of the Cauchy Problem for a System of Oscillators on a 2D-Lattice with Power Potentials

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Abstract

We consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two-dimensional integer-valued lattice. We prove a result on the existence and uniqueness of global solutions of the Cauchy problem for such systems with power potentials. Moreover, a result on the nonexistence of global solutions is obtained.

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Authors and Affiliations

  1. Mykhailo Kotsyubynskyi Vinnytsia State Pedagogical University, Vinnytsia, Ukraine

    Sergiy M. Bak

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  1. Sergiy M. Bak
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Correspondence to Sergiy M. Bak.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 4, pp. 465–476 October December, 2019.

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Bak, S.M. Global Well-Posedness of the Cauchy Problem for a System of Oscillators on a 2D-Lattice with Power Potentials. J Math Sci 246, 593–601 (2020). https://doi.org/10.1007/s10958-020-04765-6

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  • DOI: https://doi.org/10.1007/s10958-020-04765-6

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